Conventionally, balance wheels for watches are made principally from metal. In a horological mechanism, a balance spring (e.g. hairspring) is arranged to oscillate the balance wheel, ideally with an isochronous period of oscillation.
The period of oscillation T of a horological mechanism is given by the equation
                              T          =                      2            ⁢            π            ⁢                                          1                G                                                    ,                    1      where I is the moment of inertia of the balance wheel and G is the torque of the balance spring. Further,I ∝Mr2,  2where M is the mass of the balance wheel and r is its radius of gyration.
External influences such as temperature change and magnetism can affect properties of the balance spring and balance wheel which can cause variations in the period of oscillation. For the horological mechanism to be accurate in use, e.g. permit accurate time keeping, it is necessary to compensate for these external influences.
The effects of a temperature change on the balance wheel and the balance spring are not the same. Whereas the balance wheel is in general only affected by thermal variations, which affect its physical dimensions, commonly employed balance springs are typically affected by both thermal and magnetic variations, which affect both their physical dimensions, and their elasticity (Young's modulus).
Thermal compensation in a horological mechanism relates to controlling the relationship between the thermal evolution of I and G to provide a constant value of T across a temperature range of interest. The most successful previous attempts at this were C. E. Guillaume's bimetallic compensating balance wheel and steel balance spring system (invented in 1912) and Hamilton's precision ferro-nickel based spring alloy in conjunction with a steel and invar ovalising balance wheel (invented in 1943). Both these attempts required the use of materials which despite their useful thermal characteristics (e.g. the ferro-nickel alloys with an abnormal Young's modulus evolution) were sensitive to magnetism. This latter influence disturbs the Young's modulus stability and causes negative effects to the precision (isochronism) of these devices.
The inventor's earlier patent publications WO 2004/008259 and WO 2005/040943, incorporated herein by reference, disclose techniques for compensating for the effects of both temperature change and magnetism.
WO 2004/008259 describes balance spring materials which enable the thermal and magnetic effects to be greatly reduced or eliminated, thereby permitting greater precision. In particular, this publication disclosed selecting materials which would permit a change in period ΔT caused by a rise in temperature of 1° C. to tend to zero. ΔT can be written as
                                          Δ            ⁢                                                  ⁢            T                    =                                    α              1                        -                                          3                2                            ⁢                              α                2                                      -                                          1                2                            ⁢                                                δ                  ⁢                                                                          ⁢                  E                                E                                                    ,                    3      
where α1 is the coefficient of thermal expansion of the balance wheel, α2 is the coefficient of thermal expansion of the balance spring and
      δ    ⁢                  ⁢    E    Eis the thermoelastic coefficient of the balance spring. WO 2004/008259 described materials with small values for α1 and α2 (e.g. less than 6×10−6 K−1) and a small value for
            δ      ⁢                          ⁢      E        E    ,which permitted ΔT to be reduced more readily.
WO 2005/040943 describes a thermally compensating non-magnetic balance wheel for use in conjunction with a thermally stable non-magnetic balance spring in a mechanical oscillator system in a horological or other precision instrument, the balance wheel including components of two different materials having different coefficients of thermal expansion, the components being arranged to give equipoise to the balance wheel and to cause a decrease in the moment of inertia of the balance wheel with an increase in temperature, wherein the decrease in the moment of inertia is arranged to compensate for changes in the elasticity of the balance spring caused by the increase in temperature. A thermally stable spring is a spring made from a material having a low thermal expansion coefficient, e.g. of a material disclosed in WO 2004/008259.